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Teaching Mathematics for Relational Understanding

Thesis Info

Author

Mir, Raheela

Department

Institute for Educational Development, Karachi

Program

MEd

Institute

Aga Khan University

Institute Type

Private

City

Karachi

Province

Sindh

Country

Pakistan

Thesis Completing Year

1999

Thesis Completion Status

Completed

Subject

Education

Language

English

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727987792

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Teaching mathematics in Pakistan is done in a very traditional way and requires students to passively follow pre-ordained rules transmitted by the teacher. The consequence of this is that students are able to get good marks in examinations by memorizing certain rules. After the completion of each year's academic session, students memorize new things and often forget whatever they covered the previous year. In this study, I have attempted to introduce Relational Understanding' for the teaching of mathematics at the primary level in the government schools. The purpose of the study was to investigate what teachers can realistically do to develop their students relational understanding of mathematics. The study was based on the qualitative paradigm of research and designed as an action research, with data collection occurring in three stages. At the pre-intervention stage, semi-structured interviews, classroom observation and a test were conducted to examine the current situation of mathematics in the selected school. At the intervention stage, different ways of developing students' relational understanding were introduced. For example, group work was used so that every student could participate in discussions; I involved students in problem-solving activities to develop their thinking and reasoning power; I used concrete material for the clarification of abstract mathematics concepts. I strove to see how the new approach worked, what problems and challenges teachers and students face in the implementation of innovations and how the new approach affects teachers' teaching, and likewise, students' learning. In the post-intervention stage, students and teachers were interviewed to assess their perceptions about new pedagogy. One of the major findings of the study was that teaching of mathematics through the method of relational understanding can significantly improve the quality of teaching and learning in the mathematics classroom. Unfortunately, teachers' lack of awareness and inadequate knowledge hinders the implementation of relational understanding in the classroom. Recommendations are presented to remove the obstacles that are likely to cause some problems in the implementation of relational understanding.
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لینی میسن

لینی میسن

            ماہ گذشتہ میں سائنٹفک رسالوں نے دنیا کے فربہ ترین لڑکے کی خبرِ وفات شائع کی ہے، اس کا نام لینی میسن تھا، وہ لیسٹر انگلستان کا باشندہ تھا، اس کا سن پندرہ سال کا تھا، اس کی کمر کی پیمائش ۲؍۱۔۱۶۴ انچ کی، سینے کی ۶۹ انچ کی، اور ران کی ۳۸ انچ کی تھی، اس کی وفات کے بعد بلحاظ فربہی اس کی جانشینی کا قریمۂ انتخاب امریکہ کے ایک ہشت سالہ لڑکے کے پر پڑا ہے۔ (اپریل ۱۹۲۰ء)

 

منهج الشيخ محمد شريف الله في تفسيره البديع في معرفة معاني كلام ربنا السميع

The Message of Allah (Qura'n) is error free from all type of mistakes. Both wordily, literally because Allah has taken the responsibility of the protection of it. Allah has produced a chain of scholars (Mufaŝserïn) for the protection of meaning of the Holy Qura'n. These scholars have explained the meaning of every aspect and angle of the Holy Qura'n in different languages of the world in a dignified manner. By the grace of Allah and due to the hard work and sincere efforts of these scholars the Tafs┘r of Holy Qura'n is present in its original condition. In this matter the efforts of this great Scholar is worth mentioning, especially his Tafs┘r [Al-Badiĕ fĕ M┐rifa Ma┐n┘ Kalām Rabßan┐ Al-sam┘] is short but contain precise and precious points, is the master piece of literature and knowledge. In Pakistan and particular in the Punjab province he is the personality who follow the Hanafi school of thought setting aside the conflicts, with strong arguments served the Qura'n and Had┘th for his life time. Below article is critical appreciation of mention Tafs┘r.

Synthesis and Charecterization of Autochthonic Guar Gum Derivatives

The objective of this research is to introduce new green, nontoxic, cost effective derivatives of guar gum (GG-1). Guar gum is one of the important naturally occurring non-ionic polysaccharide which has incredible applications due to its rheological modifying properties in medicinal, pharmaceutical, food, textile, cosmetics, water treatment, mining, drilling, explosives, confectioneries and scores of other industrial and commercial sectors. Guar gum, also called guaran, is a galactomannan. It is primarily the ground endosperm of guar beans. The guar seeds are dehusked, milled and screened to obtain the guar gum. It is typically produced as a free-flowing, off-white powder.The adaptation of physical properties of GG-1 & GG-2 can improve and diversify its commercial applications. GUAR GUM x In this project, novel and efficient synthesis of five different new derivatives (120-124) of guar gum were done by insitu activation of cinnamic acid, ferulic acid, caffeic acid, coumaric acid and hydrocinnamic acid by coupling with dicyclohexylcarbodiimide (DCC) and N, N-dimethylaminopyridine (DMAP). Effect of temperature, concentration of reactants and time interval plays important role for determining DS value of guar esters. Reaction conditions were optimized for each reaction. Antioxidant potential was examined by DPPH method. A rapid method for protecting the hydroxyl group in sterically hindered gum has been developed by using microwave assisted synthesis (MAS). A novel and efficient synthesis of different guar gum derivatives (126-133) such as acetate, butyrate propionate, maleate, succinate, phthalate, citraconate and glutarate have been developed by microwave irradiation. The maximum ester formation was successfully achieved in 15minutes at 600W by using iodine and DMAP as a reaction promoter. Gum ester formation was obtained by concentration variation at different time intervals. The products were characterized by IR and NMR spectroscopy and SEM. Moreover, degree of substitution was also calculated for each experiment by titration method. First time fatty acid esters (C5-C18) were formulated (136-145) via acid chloride route. Reaction proceeded in two steps. First step involves conventional synthesis of fatty acid chlorides (135a-135j) by reacting corresponding acid with slight excess of thionyl chloride (134). Second step involves esterification of free hydroxyl group of GG-2 with acid chloride; as a result novel derivatives (136-145) with fascinating thickening and emulsifying properties were obtained which might be promising candidate for cosmetic and food industry. Physical properties were examined like solubility, surface morphological study, swelling behavior, gelation index etc. Different spectroscopic techniques were used for structure elucidation. In situ hydrolysis of guar esters were done in DCl during NMR experiments due to the poor solubility of guar derivatives. Guar derivatives with variable degree of substitution (DS) were prepared and were confirmed by FT-IR spectroscopy, presence of carbonyl signal confirmed the formation of guar ester. Further structural elucidation was done by 1H-NMR .Surface morphological study of guar esters was done by scanning electron microscopy (SEM) which showed networking in guar derivatives which xi enhanced when degree of substitution increased. Degree of substitution was determined quantitatively by titration method for each derivative.